Oh it's not the definition of rank I am concerned with. I wanted to know if using rank was a good method to answering the question "Show that a linear map T:R4->R4 has one of the following as its image: just the origin 0, a line through 0, a plane through 0, a copy of R3 through 0, or all of R4. "
Homework Statement
Show that a linear map T:R4->R4 has one of the following as its image: just the origin 0, a line through 0, a plane through 0, a copy of R3 through 0, or all of R4.
Homework Equations
N/a
The Attempt at a Solution
I'm not sure I'm even understanding the...